No. USB strictly distinguishes between host and device roles. A few chips have functional blocks capable of performungperforming either role, but the 8u2/16u2 are not examples of this.
Typical USB serial converters like the FT232, CP210x, CH340, PL2303, etc are also strictly devices and incapable of being hosts
There are inexpensive host-capable MCUs like the Kinetis KL25Z, but to use them in their cheapest form you would need a different software approach (for example mbed rather than Arduino) and a lot more personal effort. The Teensy-LC is related, but you pay a premiummore for the Arduino code loading helper on it than for the MCU that runs your program itself.